MATHEMATICS HIGH SCHOOL

Given the sequence 5; 12 ; 21; 32; .... a determine the formular for the nth term of thw sequance . 2 determine between which two consecutive terms in the sequance the difference will equal 245 sketch the graph to represent the second difference

Answers

Answer 1
Answer:

The nthterm for the sequence is 4n + n².

The two consecutiveterms in the sequence where the difference will be 245 are 120 and 121.

What is a sequence?

A sequence is a group of numbers where there is a relation between each consecutive value.

We have,

5, 12, 21, 32,

We see that,

The difference between the consecutive numbers is 7, 9, 11, 13, 15,

We can make a formula for the nth term.

4n + n²

Where n = 1, 2, 3, 4, ,,,,

Now,

Let the two consecutiveterms be n and (n +1).

4(n + 1) + (n + 1)² - 4n - n² = 245

4n + 4 + n² + 2n + 1 - 4n - n² = 245

4 + 2n + 1 = 245

2n + 5 = 245

2n = 240

n = 120

And,

n + 1 = 121

So,

The two consecutiveterms in the sequence where the difference will be 245 are 120 and 121.

Thus,

The nthterm for the sequence is 4n + n².

The two consecutiveterms in the sequence where the difference will be 245 are 120 and 121.

Learn more about sequence here:

brainly.com/question/10396151

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Answer 2
Answer: First difference
12-5 = 7
21-12 = 9
32-21 = 11

Second difference
9-11 = 2
11-9 = 2

second difference is constant so it could defined by quadratic formula,
u(x) = ax^2 + bx + c
because 2a = Second difference = 2
so a = 1
then u(x) = x^2 + bx + c

build equations from known values to find b and c
for x=1, u(1) = 5 = 1^2 + b(1) + c
b + c = 4 ...(1)

x=2, u(2) = 12 = 2^2 + b(2) + c
2b + c = 8 ... (2)

solve b = 4, c =0
so u(x) = x^2 + 4x ... formula for n term (i use x not n here)

difference between consecutive term is 245, we have
245 = u(x+1) - u(x)
245 = (x+1)^2 + 4(x+1) - (x^2 + 4x)
245 = x^2 + 2x + 1 + 4x + 4 - x^2 - 4x
245 = 2x + 5
x = 120
it's between term 120 and 121

graph is y=2

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Answers

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Answers

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Answers

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Answers

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Answers

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Step-by-step explanation:

On a standardized science test, the seniors at Fillmore High School have a mean score of 430 with a standard deviation of 90.For random samples of 100 seniors, what interval centered on the mean of the sampling distribution captures 68% of the mean scores? If necessary, round to the nearest tenth. Enter the interval from least to greatest.

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Answers

Answer:

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Step-by-step explanation:

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Hope this helps!

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